Sound transmission. Characterization and properties of single walls and floors - Building Acoustics - page 259

4 ρ c 4 ρ c

p

2

=

00

⋅ = ⋅ W a

00

F

2

, (6.115)

A A

where A is the total absorption area of the room. We further assume that, imbedded into
another wall of the room, we have a small (in relation to the wavelength) mass-controlled
piston of mass m and area S . The resulting force F p on the piston, caused by the sound
field in the room, induces a piston velocity u ps given by

1 1

2

uF =⋅ = Sp 2 ⋅ . (6.116)

ps p

ω m ω m

This enables us to write

u

2

2

8 ρ cS

ps

=⋅ a

00

, (6.117)

2 2 2

F A m ω

where the angular frequency ω is understood to be the centre frequency of a band broad
enough to give diffuse field conditions.

a) b)

F

p

u' ps p '

u ps

u p

F

Figure 6.32 Sketch of a room used for a thought experiment. a) A force F is driving a plate being part of a wall,
b) A monopole source drives the plate via the sound field in the room.

In the next part of the thought experiment (see Figure 6.32) , we shall drive this
piston by the same point force used to drive the plate. The piston then gets a velocity u' ps ,
thereby radiating a power W ´ into the room equal to the power from a piston in a baffle.
At low frequencies, the piston will act like a monopole source and the power may be
written (see sections 3.4.1 and 3.4.4)

2

2 2 2

ρ ck ρ ck ρ ck ⎛ F ⎞

( )

2

W ′ = ⋅ Q ′

2

= ⋅ S u

ps '

= ⋅ ⎜ S . (6.118)

00 00 00

⎟

2 π 2 π 2 π ω m

⎝ ⎠

In the last expression we have inserted the relationship between the force and the
resulting velocity of the piston. This power will again set up a sound field in the room
having a sound pressure p ´ given by